Write paper on analyzing female height data setq
This project will cover topics from chapters 7 through 10. You will be turning in a paper that should include
section headings, graphics and tables when appropriate and complete sentences which explain all analysis
that was done in addition to all conclusions and results. You will be performing an analysis on female heights,
given of set of 30 heights that were randomly obtained. For this project, it is necessary to know that the
average height for women is assumed to be 65 inches with a standard deviation of 3.5 inches. You will use
these numbers in some of your calculations.
Steps:
1.Download the data.
2.Find Elizabeth in the data and, given the population mean and standard deviation, calculate:
a. The z-score for Elizabeth (easiest to be done by hand).
b.The probability that a randomly selected female is shorter than Elizabeth.
c.The probability that a randomly selected female is taller than Elizabeth.
d.Interpret each of these in a sentence (3 full sentences).
e. HINT: for this step you should use the mean and standard deviation that are given in the paragraph above
“Steps”. You should not use a sample mean or sample standard deviation calculated from the data given.
3.As you know, a random sample of 30 women’s heights was obtained. Describe the sampling distribution. Use
a full sentence here to describe the sampling distribution.
HINT: See the Chapter 8 Lecture Notes Key if you are stuck. You will not use the raw data yet.
4.In StatCrunch or Excel, find and state the mean of the 30 women’s heights that were provided (round to two
decimal places). Then (using the values from step 3), calculate the probability that a random sample of 30
women’s heights would result in a mean that was the value you found or more. Use this probability in a full
sentence.
- Explain how what you just calculated in step 4 relates to the question you were asked in step 2c. Why is the
probability in step 4 lower than that in step 2? - For this step, please work under the assumption that we do not know the population mean and standard
deviation (and in fact, if we are running this test, it means that we are not sure of these values). Construct a
95% confidence interval for the average height of a female. Interpret this confidence interval. HINT: You can
use the “with data” option in StatCrunch to do this calculation. - It is a researcher’s belief that the average height of females has increased since theaverage value of 65
inches was reported. Using the sample of 30 female heights,conduct a hypothesis test at the .05 level that
tests whether or not this researcher mightbe correct. You must state the null and alternative hypotheses as well
as the p-value andan interpretation of what this means. HINT: You can use the “with data” option inStatCrunch
to do this calculation. - How do the results from steps 6 and 7 relate to one another? HINT: does the true mean(given above these
steps) lie in the interval found in step 6? How is this confirmed bythe result in step 7? - Put everything together into an organized paper.
Sample Solution